Airlines Exploit The (Peter) Diamond Paradox?

Airlines are increasingly pushing and prodding travelers to book flights through their own websites, where they can sell more services like in-flight entertainment and add-ons like hotel reservations. They also bypass paying a commission to websites that book plane tickets.

For consumers, this means that the hunt for the lowest fare has become more difficult as the number of places where they can comparison-shop has dropped. In many cases, they just give up.

Peter Diamond has a classic paper A Model of Price Adjustment in the Journal of Economic Theory in 1971. Diamond shows that even an infinitesimal search cost can lead to monopoly pricing rather than competitive pricing because of a hold up problem. Suppose there is no search cost and two firms are selling an identical good. The logic of (Bertrand) competition means they will both end up pricing at cost. At any higher price, one firm can undercut the other and capture the entire demand rather than half the demand and double its profit.

Instead suppose there is a small search cost e>0 a consumer must pay to discover the price. Pricing at cost is no longer an equilibrium – one firm can raise its price by almost e. The consumer discovers the higher price once he enters the store. But going to the other store to get a lower price involves a transactions cost of e anyway. So, it is better to submit to hold-up and pay the higher price. This logic obtains at all prices lower than the monopoly price. At that point you do not want to raise the price any more as consumers simply stop buying at a rate than makes further price increases lead to lower profits. So, a small search cost reverses the intuition about pricing completely.

2 comments

OK, I guess I should read the Diamond paper. But from your description of it, the monopoly price does not sound like an equilibrium either.

Suppose the monopoly price is well above marginal cost (10x e above cost for example). If there are two firms sharing the market at the monopoly price, then it makes sense for one to drop its price by (a little bit more than) e. Then it gets the whole market at a profit of (a little bit less than) 9e per unit sold, instead of half the market at a profit of 10e. Then the other firm responds and down you go…until p = MC + 2e when this is no longer profitable.

There’s just no equilibrium between this bound and the monopoly profit, surely. Between them you can always make more money either by putting prices up by less than e or putting them down by more than e.

But that does not mean you’ll get monopoly prices, as the article kind-of implies.